# Bias and Unbias

Question: Robin and Williams are playing a game. An unbiased coin is tossed repeatedly. Robin wins as soon as the sequence of tosses HHT appears. Williams wins as soon as the sequence of tosses HTH appears. The game ends when one of them wins. What are the probabilities of winning for each player? . . … Continue reading Bias and Unbias

# Life and luck

Question: You and your friend are caught by gangsters and made to play a game to determine if you should live or die. The game is simple. There is a deck of cards and you both have to choose a card. You can look at each other’s cards but not at the card you have chosen. … Continue reading Life and luck

# All men must die

Question: One day, an alien comes to Earth. Every day, each alien does one of four things, each with equal probability to: (i) Kill himself (ii) Do nothing (iii) Split himself into two aliens (while killing himself) (iv) split himself into three aliens (while killing himself) What is the probability that the alien species eventually dies out … Continue reading All men must die

# Dodge ball

Question: You are playing a game of dodge ball with two other people, John and Tom. You're standing in a triangle and you all take turns throwing at one of the others of your choosing until there is only one person remaining. You have a 30 percent chance of hitting someone you aim at, John … Continue reading Dodge ball

# Two pills

Question: A man has to take two pills each day, at the exact same time or he will die. If he only takes one or he takes two of the same pill he will die. Both medications look the same and are the same weight. One day he drops both open pill bottles scattering the … Continue reading Two pills

# Two bullets

Question: Two bullets are put into a gun's round barrel consecutively, which has capacity of 6. The gun is shot once, but no bullet is fired. Does rolling the barrel (shuffling) before next shot increase the probability of firing a bullet? . . C A P T A I N I N T E R … Continue reading Two bullets